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GATE | GATE-CS-2015 (Set 3) | Question 65

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In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following:

“The result of the toss is head if and only if I am telling the truth.” 

Which of the following options is correct?

(A) The result is head
(B) The result is tail
(C) If the person is of Type 2, then the result is tail
(D) If the person is of Type 1, then the result is tai


Answer: (A)

Explanation:

“The result of the toss is head if and only 
 if I am telling the truth.” 


If the person is of Type 1 who always tell truth, then result must be head.

If the person is of Type 2 who always tell lie, then result must be head.

Negation of a sentence of the form "X is true if and only if Y is true" is 
"Either X is true and Y is false, or X is false and Y is true."

Refer: http://math.stackexchange.com/questions/10435/negation-of-if-and-only-if

Which means "Either toss is head and I am not telling truth, or toss is tail
and I am telling truth".

Since the person always lie, it is "Either toss is head and I am not telling truth"


Quiz of this Question


Last Updated : 28 Jun, 2021
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